a) Let E be a nonempty subset of X. Prove that a is a cluster point of E if and only if for each r > 0, E Br(a) (a) is nonempty. b) Prove that every bounded infinite subset of R has at least one cluster point.
a) Let E be a nonempty subset of X. Prove that a is a cluster point of E if and only if for each r > 0, E ∩ Br(a) \ (a) is nonempty.
b) Prove that every bounded infinite subset of R has at least one cluster point.
b) Prove that every bounded infinite subset of R has at least one cluster point.
This problem has been solved!
Do you need an answer to a question different from the above? Ask your question!
Answer
a) Surely a set which has infinitely many points is nonempty. Conversely, if E B s (a) n {a} is …View the full answer
Related Book For 
